# Mensuration: Essential Skills for O Level Math Students

Mastering Mensuration

## What is Mensuration?

Mensuration is the branch of mathematics that deals with the measurement of geometric figures and their parameters such as length, area, volume, and angles. It involves the study of formulas and techniques for quantifying the size, shape, and spatial dimensions of two-dimensional and three-dimensional objects. In essence, mensuration provides the mathematical framework for calculating and analyzing the properties of geometric shapes in both theoretical and practical contexts.

## Mensuration in the O levels

For secondary school students, the learning objectives in the topic of mensuration are in the syllabus as follows:

Students should be able to find the area of parallelogram and trapezium

–   problems involving perimeter and area of composite plane figures

–   volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere

–   conversion between cm2 and m2 , and between cm3 and m3

–   problems involving volume and surface area of composite solids

–   arc length, sector area and area of a segment of a circle

–   use of radian measure of angle (including conversion between radians and degrees)

## Mensuration Formula Cheat Sheet

There are only a few formulas that are commonly encountered in O Levels Singapore, master these formulas and apply them to the questions accordingly:

Area of a Rectangle: A = length × width

Perimeter of a Rectangle: P = 2 × (length + width)

Area of a Square: A = side × side (or A = side²)

Perimeter of a Square: P = 4 × side

Area of a Triangle: A = ½ × base × height

Perimeter of a Triangle: P = side1 + side2 + side3 (sum of all sides)

Area of a Circle: A = π × radius²

Circumference of a Circle: C = 2 × π × radius

Volume of a Cuboid: V = length × width × height

Surface Area of a Cuboid: SA = 2 × (length × width + width × height + height × length)

Volume of a Cylinder: V = π × radius² × height

Surface Area of a Cylinder: SA = 2 × π × radius × (radius + height)

Volume of a Prism: V = area of base × height

Surface Area of a Prism: SA = sum of the areas of all faces

Volume of a Pyramid: V = ⅓ × area of base × height

Surface Area of a Pyramid: SA = sum of the area of the base and the lateral faces

Volume of a Sphere: V = ⁴⁄₃ × π × radius³

Surface Area of a Sphere: SA = 4 × π × radius²